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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 200277x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 200277.x1 | 200277x1 | \([1, -1, 0, -72882, 6208447]\) | \(2433138625/467313\) | \(8222974041148713\) | \([2]\) | \(1032192\) | \(1.7710\) | \(\Gamma_0(N)\)-optimal |
| 200277.x2 | 200277x2 | \([1, -1, 0, 148203, 36408658]\) | \(20458415375/44449713\) | \(-782149942619851113\) | \([2]\) | \(2064384\) | \(2.1176\) |
Rank
sage: E.rank()
The elliptic curves in class 200277x have rank \(0\).
Complex multiplication
The elliptic curves in class 200277x do not have complex multiplication.Modular form 200277.2.a.x
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
